If I filed a do it yourself divorce, the judge granted the divorce but I didn't sign the final decree, do I need to do anything else?

You don't have to change your name, but you should have signed off on the final decree. I am surprised that the judge signed it. Did your ex sign it? If there is a procedural error, it can be corrected, but I'd hire an attorney to look into it now, so you can move on with your life.

Contact the court clerk and ask for a certified copy of the divorce judgment.. it might cost $10 or so if you cannot get a certified copy of the Written Court Judgment of Divorce signed by the judge you are not yet divorced. As to changing your name.

Generally speaking if a judge has signed your decree of dissolution, and it has been filed with the clerk of the court, your only potential obligation would be to mail a copy of the decree to the opposing party. My experience with what sounds like a default dissolution situation (you filed the petition and supporting documents, he either signed an acceptance of service or was served, he filed no response, and you filed an application and affidavit of default), then the court would have mailed the copy in a self addressed stamped envelope you provided at the default hearing. If the decree includes a provision for a change of your name then you will probably have to get a certified copy of the decree to show to DMV, to get your name changed on your driver's license. It may be that a simple copy of the decree will be sufficient for Social Security. These are positive steps that you have to take to get your name changed on official records her in Arizona.

If the judge signed a final judgment of divorce, that is all that you need. If he verbally granted a divorce but has never signed a judgment, you need to prepare a proper judgment and have the judge sign it. Whether you have to change your name depends upon what the final judgment says. If it is silent as to your name change, your name did not change. If your Judgment hasn't been signed yet, you should be very careful to make sure that all of the paperwork is prepared properly. Consider hiring an attorney just to review it (this should not cost much). The Judgment is probably the single most important document/contract of your life, and mistakes can be very costly.

If the Judge hasn't signed it, then the divorce isn't final

You don't sign the final decree, the judge does. If the judge signed the decree, the divorce is final. You could try and ask the court to amend the decree to allow your name change. If the court doesn't do that, then you will have to file separately.

The only signature which really counts on a divorce decree is that the judge granting it. Once it entered its terms are in effect. If you have entered an order with the provision that changes your name is legally changed and I would suggest that you either active accordance with the judgment or seek to have the judgment modified.